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Big Ideas Math: Modeling Real Life, Grade 8

BI

Big Ideas Math: Modeling Real Life, Grade 8 View details

3. Volumes of Spheres

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Exercise 23 Page 444

The volume of a composite solid is either the sum or difference between the volumes of the individual solids.

About 1206.4 cubic feet

Practice makes perfect

Consider the given composite solid.

The composite solid is formed by a cylinder and a cone. To find the volume, remember that the volume of a composite solid is either the sum or difference between the volumes of the individual solids. Let's do one at time!

Volume of Cylinder

Recall the formula for the volume of a cylinder. V_(cylinder)=Bh Here, B represents the area of the base and h is the height of the cylinder. The base is a circle, so we can find the area by recalling the area of a circle with radius r. B=π r^2 In our case, the diameter is 16 feet which means that the radius is 8 feet. Then, we can calculate the base area of the cylinder by substituting r= 8 into the above formula.

B= π r^2

r= 8

B = π ( 8)^2

Calculate power

B= π(64)

Multiply

B= 64π

Now that we know the area of the base, we can calculate the volume of the cylinder by substituting B= 64π and h= 4 into the volume's formula.

V_(cylinder)=Bh

B= 64π, h= 4

V_(cylinder)= 64π( 4)

Multiply

V_(cylinder)= 804.247719 ...

Round to 1 decimal place(s)

V_(cylinder) ≈ 804.2

The volume of the cylinder is about 804.2 cubic feet.

Volume of Cone

Now, we will use the formula for the volume of a cone. V_(cone)=1/3π r^2h Let's substitute r= 8 and h= 6 into the volume's formula.

V_(cone)=1/3π r^2h

r= 8, h= 6

V_(cone)=1/3π ( 8)^2( 6)

Calculate power

V_(cone)=1/3π(64)(6)

Multiply

V_(cone)=1/3π(384)

MoveRightFacToNum

a/c* b = a* b/c

V_(cone)=384π/3

Calculate quotient

V_(cone)=128π

Use a calculator

V_(cone)=402.133859 ...

Round to 1 decimal place(s)

V_(cone)≈ 402.1

The volume of the cone about 402.1 cubic feet. Now that we have the volume of each solid, we can add them to find the volume of the composite solid. V= V_(cylinder) + V_(cone) → V≈ 1206.4 ft^3

Subchapter links

Try It p.440-441

Self-Assessment for Concepts & Skills p.441

Self-Assessment for Problem Solving p.442

Review & Refresh p.443

Concepts, Skills, & Problem Solving p.443-444